Transportation Engineering: Quick Revision Notes

 

Alignment

Survey and Planning Stages

1. Map Study
2. Reconnaissance
3. Preliminary Survey
   • Finalization of the centerline of the road
4. Detailed Survey
   • Alignment located on the ground
   • Soil sampling

Key Maps

• Key Map: Important points (e.g., Google Maps)
• Index Map: Topography

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Geometric Design

Road Cross-Section Elements

• Carriageway
• Formation Width or Roadway
• Right of Way or Land Width

Cross Slope (x) Based on Terrain Type

Terrain Type	Cross Slope (x)
Plain	0 to 10
Rolling	10 to 25
Mountain/Hilly	25 to 60
Steep	> 60

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Friction Coefficients

• Longitudinal Coefficient of Friction = 0.25
• Lateral Coefficient of Friction = 0.15

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Pavement Characteristics

Surface Conditions and Tire Type

• Dry Surface → Old Tyre
• Wet Surface → New Tyre

Pavement Unevenness

• Unevenness Index = Cumulative vertical undulations per unit length
• For Good Pavement = 150 cm/km

Instruments Used

• Roughometers
• Bump Indicator

Camber

Types of Roads and Camber Slopes

Road Type	Camber Slope for Heavy Rain (%)	Camber Slope for Light Rain (%)
Concrete Road & High-Type Bituminous Road	1 in 50	1 in 60
Thin Bituminous Road	1 in 40	1 in 50
Gravel Road & WBM (Water Bound Macadam) Road	1 in 33	1 in 40
Earth Road	1 in 25	1 in 33

Camber Curve Equation

$$y=\frac{2x^2}{\mathrm{nw}}$$

• Slope: 1 in n
• Gradient: 1V: nH

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Vehicle and Roadway Dimensions

• Maximum width of a vehicle = 2.44 m
• Width of a single lane = 3.75 m
• Width of the median = 3.5 m
• Two-lane road with raised kerb = 7.5 m
• Intermediate carriageway = 5.5 m
• Medians = 5 m
• Shoulders = 2.5 m
• Kerb height = 15 cm
• Guardrails required if embankment height >3 m

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Land Width for National Highways (NH)

• Normal width = 45 m
• Maximum width = 60 m

Typical Cross-Section of a Highway (Sketch Included in Notes)

• Roadway width variations:
  • 45 m
  • 80 m
  • 150 m
• Includes boundaries like building lines and ample line

Gradient

• Ruling Gradient → Design gradient
• Limiting Gradient → Steeper than the ruling gradient
• Minimum Gradient → Required for drainage purposes
• Exceptional Gradient → Greater than the limiting or minimum gradient

Grade Compensation

• If grade ≤ 4% → No compensation required
• Grade Compensation Formula: $$GC = \min\left(\frac{30 + R}{R}, \frac{75}{R}\right)$$
  

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Sight Distance

Stopping Sight Distance (SSD)

$$SSD=Vt+\frac{V^2}{2g(f\pm n)\mathrm{\gamma }}$$

• Perception-reaction time = 2.5 sec
• Lag distance: $Vt$
  
• Braking distance: $\frac{V^2}{2g(f \pm n) \gamma}$

Intermediate Sight Distance (ISD)

$$ISD=2\times SSD$$

Headlight Sight Distance (HSD)

$$HSD=SSD$$

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Overtaking Sight Distance (OSD)

$$OSD=V_{b}T+(V_{b}T+2S)+V_{c}T$$

• Reaction time for overtaking = 2s
• Overtaking formula derivations include:
  • $S = (0.7V_b + L)$ meters
  • $S = (0.2V_b + L)$ meters
  • Average L value = 6.1m
  • Overtaking speed formula:
    • $V_b = (V - 16)$ km/h
    • $\approx (V - 41.5)$ mps

Overtaking Zone

• Minimum length = 3 × OSD
• Desired length = 5 × OSD

Horizontal Curve

Impact Factors of Centrifugal Ratio

$$\frac{P}{W}=\frac{V^2}{g\mathrm{R}}$$

• To avoid overturning: $$\frac{b}{2h}>\frac{V^2}{g\mathrm{R}}$$
• To avoid skidding: $$f>\frac{V^2}{g\mathrm{R}}$$
• If $\frac{b}{2h} < \frac{V^2}{gR}$, vehicle overturns before skidding

• If $f < \frac{b}{2h}$, vehicle skids before overturning

Superelevation Formula

$$e+f=\frac{V^2}{2g\mathrm{R}}$$

• In km/h: $$\frac{V^2}{127R}$$
• Alternative form: $$\frac{(0.75V{)}^2}{gR}=\frac{V^2}{225\mathrm{R}}$$

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Maximum Superelevation (e$_{max}$)

Terrain Type	Maximum Superelevation
Plain & Rolling	7%
Hilly	10%

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Extra Widening (We)

$$W_e = W_m + W_ps$$

• Mechanical Widening:

  $$W_m=\frac{n{L}^2}{2\mathrm{R}}$$
  • L$^2$/2R accounts for off-tracking
  • n = Number of lanes

• Psychological Widening:

  $$W_{p}s=\frac{V}{9.5\sqrt{\mathrm{R}}}$$

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Widening Guidelines Based on Radius (R):

• If $R \leq 50m$ → Provide extra widening only on the inner side
• If $R > 50m$ → Distribute widening equally on both sides

Setback Distance (m)

• Length (fill) > Stopping Sight Distance (SSD) (s)
• Formula for Setback Distance (m): $$m=\frac{s^2}{8\mathrm{R}}$$
• If $L < S$, then: $$m=\frac{L(2S-L)}{8\mathrm{R}}$$

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Transition Curve

• Ideal transition curve → Spiral or Clothoid
• Condition: $$LR = \text{constant}$$
  

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Length of Transition Curve

• General Formula:

  $$L=\frac{V^3}{C\mathrm{R}}$$

• Constant (C) Calculation:

  $$C=\frac{80}{75+\mathrm{V}}$$

• Rate of Change of Centrifugal Acceleration:

  $$0.5<C<0.8$$

• Shift Formula:

  $$\text{Shift} = \frac{L^2}{24R}$$

Length of Superelevation Transition Curve

• Formula:

  $$L=\frac{eRN}{N}\text{or}\frac{eNW}{\mathrm{2}}$$
  • N = Rate of change of superelevation

• For Different Terrain Types:

  $$L=\frac{2.7V^2}{R}\text{(Plain/Rolling)}$$$$L=\frac{V^2}{R}\text{(Steep)}$$

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Summit Curves

For Stopping Sight Distance (SSD)

• If $L > S$:

  $$L=\frac{N{S}^2}{(2H+2h{)}^2}=\frac{N{S}^2}{\mathrm{4.4}}$$

• If $L < S$:

  $$L = 2S - \frac{(\sqrt{2H + 2h})^2}{N} = 2S - \frac{4.4}{N}$$

• Height values:

  • H = 1.2m
  • h = 15cm

For Overtaking Sight Distance (OSD) or Intermediate Sight Distance (ISD)

• If $L > S$: $$L=\frac{N{S}^2}{\mathrm{9.6}}$$
• If $L < S$: $$L=2S-\frac{9.6}{\mathrm{N}}$$

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Gradient Changes

• Gradient Change Formula: $$V_N=N_1-N_{\mathrm{2}}$$
• Sign Convention:
• Ascending gradient → Positive (+ve)
• Descending gradient → Negative (-ve)

Valley Curve

Ideal Shape: Cubic Parabola

For Comfort:

$$L=2\sqrt{\frac{N{V}^3}{C}}$$

For Stopping Sight Distance (SSD):

• If $L > S$: $$L=\frac{N{S}^2}{2h+2S\tan \mathrm{\alpha }}$$
• If $L < S$: $$L=2S-\frac{2h+2S\tan \alpha }{\mathrm{N}}$$